A NEW NUMERICAL APPROACH OF SOLVING FRACTIONAL MOBILE-IMMOBILE TRANSPORT EQUATION USING ATANGANA-BALEANU DERIVATIVE

Reetika Chawla; Komal Deswal; Devendra Kumar

doi:10.11948/20230044

2023 Volume 13 Issue 5

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Reetika Chawla, Komal Deswal, Devendra Kumar. A NEW NUMERICAL APPROACH OF SOLVING FRACTIONAL MOBILE-IMMOBILE TRANSPORT EQUATION USING ATANGANA-BALEANU DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2874-2895. doi: 10.11948/20230044

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Reetika Chawla, Komal Deswal, Devendra Kumar. A NEW NUMERICAL APPROACH OF SOLVING FRACTIONAL MOBILE-IMMOBILE TRANSPORT EQUATION USING ATANGANA-BALEANU DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2874-2895. doi: 10.11948/20230044

A NEW NUMERICAL APPROACH OF SOLVING FRACTIONAL MOBILE-IMMOBILE TRANSPORT EQUATION USING ATANGANA-BALEANU DERIVATIVE

1.
Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan-333031, India

Author Bio: Email: komaldeswal94@gmail.com(K. Deswal); Email: dkumar@pilani.bits-pilani.ac.in(D. Kumar)
Corresponding author: Email: reetika.chawla285@gmail.com(R. Chawla)

Abstract

Abstract

A numerical scheme comprising the Crank-Nicolson difference sch-eme in the temporal direction and cubic trigonometric $B$-spline method in the spatial direction is examined for the numerical solution of the variable coefficient time-fractional mobile-immobile solute transport equation. The time-fractional derivative is evaluated using the Atangana-Baleanu Caputo derivative. The equation has advection, dispersion, and reaction coefficients that can be influenced simultaneously by space and time variables. The present numerical scheme is unconditionally stable and second-order convergent in the temporal and spatial directions. Several test problems are solved to confirm the theoretical results.
- Atangana-Baleanu Caputo derivative /
- cubic trigonometric $B$-spl-ines /
- Crank-Nicolson scheme /
- stability /
- convergence
MSC: 26A33, 65M06, 65M12, 65M15, 65N06, 65N15, 35R11

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References

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